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We show how techniques from machine learning and optimization can be used tofind circuits of photonic quantum computers that perform a desiredtransformation between input and output states. In the simplest case of asingle input state, our method discovers circuits for preparing a desiredquantum state. In the more general case of several input and output relations,our method obtains circuits that reproduce the action of a target unitarytransformation. We use a continuous-variable quantum neural network as thecircuit architecture. The network is composed of several layers of opticalgates with variable parameters that are optimized by applying automaticdifferentiation using the TensorFlow backend of the Strawberry Fields photonicquantum computer simulator. We demonstrate the power and versatility of ourmethods by learning how to use short-depth circuits to synthesize singlephotons, Gottesman-Kitaev-Preskill states, NOON states, cubic phase gates,random unitaries, cross-Kerr interactions, as well as several other states andgates. We routinely obtain high fidelities above 99\% using short-depthcircuits, typically consisting of a few hundred gates. The circuits areobtained automatically by simply specifying the target state or gate andrunning the optimization algorithm.

Machine learning method for state preparation and gate synthesis on photonic quantum computers